Question 468534
1. (1 point) Find the probability that you will win exactly 4 times. Round answer to three places after the decimal point. 
I used the formula Pr(x-k)= c(n,k) p^k x q^ (n-k) 
so... c(10,4) (.45)^4 x (.55)^(10-4) - CORRECT
2. (1 point) Find the probability that you will win 2 or more times. Round answer to three places after the decimal point. 
P(win 2 or more times)=P(2)+P(3)+P(4)+P(5)+P(6)+P(7)+P(8)+P(9)+P(10)
The best way to solve this problem by opposite event
P(win 2 or more times)=1-P(win less then 2)
P(win less then 2)=P(0)+P(1)
THEN 
P(win 2 or more times)=1-(P(0)+P(1))
P(win 2 or more times)=1-(c(10,0)(.45)^0*(.55)^(10-0)+c(10,1)(.45)^1*(.55)^(10-1))
3.(1 point) Find the expected number of times you will win, and the standard deviation. Round both answers to three places after the decimal point. 
E(X)=np
n=10, p=0.45
E(X)=10*0.45=4.5
the standard deviation
{{{S(X)=sqrt(n*p*(1-p))}}}
{{{S(X)=sqrt(10*0.45*0.55)=sqrt(2.475)=1.573}}}